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Simplifying 11a2 + 9a + -4 = 0 Reorder the terms: -4 + 9a + 11a2 = 0 Solving -4 + 9a + 11a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.3636363636 + 0.8181818182a + a2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + 0.8181818182a + 0.3636363636 + a2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + 0.8181818182a + a2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + 0.8181818182a + a2 = 0 + 0.3636363636 0.8181818182a + a2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 0.8181818182a + a2 = 0.3636363636 The a term is 0.8181818182a. Take half its coefficient (0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. 0.8181818182a + 0.1673553719 + a2 = 0.3636363636 + 0.1673553719 Reorder the terms: 0.1673553719 + 0.8181818182a + a2 = 0.3636363636 + 0.1673553719 Combine like terms: 0.3636363636 + 0.1673553719 = 0.5309917355 0.1673553719 + 0.8181818182a + a2 = 0.5309917355 Factor a perfect square on the left side: (a + 0.4090909091)(a + 0.4090909091) = 0.5309917355 Calculate the square root of the right side: 0.728691797 Break this problem into two subproblems by setting (a + 0.4090909091) equal to 0.728691797 and -0.728691797.Subproblem 1
a + 0.4090909091 = 0.728691797 Simplifying a + 0.4090909091 = 0.728691797 Reorder the terms: 0.4090909091 + a = 0.728691797 Solving 0.4090909091 + a = 0.728691797 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + a = 0.728691797 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + a = 0.728691797 + -0.4090909091 a = 0.728691797 + -0.4090909091 Combine like terms: 0.728691797 + -0.4090909091 = 0.3196008879 a = 0.3196008879 Simplifying a = 0.3196008879Subproblem 2
a + 0.4090909091 = -0.728691797 Simplifying a + 0.4090909091 = -0.728691797 Reorder the terms: 0.4090909091 + a = -0.728691797 Solving 0.4090909091 + a = -0.728691797 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + a = -0.728691797 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + a = -0.728691797 + -0.4090909091 a = -0.728691797 + -0.4090909091 Combine like terms: -0.728691797 + -0.4090909091 = -1.1377827061 a = -1.1377827061 Simplifying a = -1.1377827061Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.3196008879, -1.1377827061}
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